CN105139392A - Improved fuzzy inference rule edge detection method - Google Patents

Abstract

The invention relates to an improved fuzzy inference rule edge detection method, belonging to the technical field of digital image processing. The improved fuzzy inference rule edge detection method comprises the steps using a fuzzy filtering method to preprocess an input noisy image to obtain a fuzzy filtering result; taking the fuzzy filtering result as input, and calculating a fuzzy edge image through the defined brightness member function, the defined darkness member function and the fuzzy rule; obtaining a threshold by substituting the fuzzy edge image and the defuzzification result into a formula; and at last obtaining the eventual edge detection result by comparing the fuzzy edge image with the threshold obtained through calculation. The improved fuzzy inference rule edge detection method can preferably suppress the noise interference to detect the edge of the image. The improved fuzzy inference rule edge detection method can effectively detect the edge of the image by improving the fuzzy inference rule edge detection algorithm through fuzzy filtering.

Description

A kind of fuzzy inference rule edge detection method of improvement

Technical field

The present invention relates to a kind of fuzzy inference rule edge detection method of improvement, belong to digital image processing techniques field.

Background technology

Permitted edge detecting technology to be in recent years suggested, wherein more and more become the focus of concern based on the technology of fuzzy entropy.Detection algorithm based on fuzzy edge is proposed by Pal and King etc. at first, makes its rim detection ability stronger because algorithm introduces obscure idea.A lot of scholar has done the research of different directions to Fuzzy Edge-detection Algorithm afterwards, the people such as S.Lu propose a kind of edge detection algorithm based on Fuzzy Neural Network System, fuzzy entropy theory is combined with nerve network system, solves the problem of neural network edge detection algorithm to noise-sensitive; The people such as L.R.Liang propose a kind of fuzzy edge sorter, obtain good rim detection effect.The people such as LimingHu propose the edge detection algorithm based on fuzzy inference rule, and this algorithm has extraordinary Image Edge-Detection ability, and has certain noiseproof feature, and especially to salt-pepper noise, its anti-noise effect clearly.But this algorithm is very sensitive for Gaussian noise, when Gaussian noise is less, desirable rim detection effect can be obtained; When Gaussian noise is larger, this algorithm can not well identify edge and noise, edge can be mistaken for noise and not extract, and causes the effect of rim detection poor.

Summary of the invention

The invention provides a kind of fuzzy inference rule edge detection method of improvement, for the rim detection of strong Gaussian noise pollution image.

The concrete steps of the fuzzy inference rule edge detection method improved that use of the present invention are as follows:

Step1, in Matlab, input piece image I (x, y), calculate difference average and the variance of each point pixel value and central point pixel value in pixel 5 × 5 window, leave three-dimensional array Ω and three-dimensional array σ respectively in ²in;

The difference average of Step2, foundation pixel value and variance, structure meets the membership function of Gaussian distribution, and carry out fuzzy filter, obtain fuzzy filter image, expression formula is as follows;

$W=e^{\left(\frac{-{\left({\mathrm{\Ω}}_{i,j,r,s}-{\mathrm{\Ω}}_{i,j}\right)}^2}{2{\mathrm{\σ}}_{i,j}^2}\right)}---\left(1\right)$

Wherein, Ω _i,jbe the average of each point pixel value and central point value differences in 5 × 5 windows, be the variance of each point pixel value and central point value differences in 5 × 5 windows, the position coordinates of pixel centered by i, j, r, s ∈ {-2 ,-1,0,1,2};

Step3, Step2 is obtained fuzzy filter image be input in Matlab, calculate this fuzzy filter image each pixel 8 neighborhood gray scale difference, leave in three-dimensional array diff, then calculate POS and the NEG value on each direction;

$\begin{array}{cc}POS\left(x\right)=\left\{\begin{array}{cc}0& diff\&le;0\\ \frac{diff}{c}& 0<diff<c\\ 1& diff\&GreaterEqual;c\end{array}\right.& NEG\left(x\right)=\left\{\begin{array}{cc}1& diff\&le;-c\\ \frac{diff}{-c}& -c<diff<0\\ 0& diff\&GreaterEqual;0\end{array}\right.\end{array}---\left(2\right)$

Wherein, POS represents brightness member function, and NEG represents darkness member function, and parameter c is the gray-scale value of gray level image;

The POS value that Step4, foundation obtain and NEG value, calculate the fuzzy entropy function of this image, this function is as follows:

$H(G,c)=\frac{1}{8\&times;W\&times;H}\underset{k=1}{\overset{8}{\&Sigma;}}\underset{i=1}{\overset{W}{\&Sigma;}}\underset{j=1}{\overset{H}{\&Sigma;}}\left(S_n\right({\mathrm{\&mu;}}_{ijk}\left)\right)---\left(3\right)$

Wherein, μ _ijkfor POS value on k direction and NEG value sum, S _n() is shannon function, and this expression formula is the function about parameter c, and by asking the maximal value of this function to determine parameter c, W and H is the wide and high of image;

Step5, according to the POS value that obtains and NEG value and 16 fuzzy rules, calculate can reflect central point and adjacent 2 all belong to the degree size at edge be subordinate to angle value μ (Q); μ is the set of μ (Q), and μ is called fuzzy edge image;

Step6, determine the gray threshold of edge extracting according to μ, computing method are as follows:

T＝max((0.8×Z ^*+0.2×μ _max),μ _local)(4)

Wherein, Z ^*for the value obtained after adopting center method de-fuzzy to fuzzy edge image, μ _maxthe maximal value of fuzzy edge image μ, μ _local3 × 3 window local mean value of fuzzy edge image μ;

Step7, to compare with gray threshold T with the gray-scale value of each pixel of fuzzy edge image μ again, when the gray-scale value of the pixel in μ is more than or equal to T, judges that this point is marginal point, the gray-scale value of this point is set to 1; When the gray-scale value of the pixel in μ is less than T, judges that this point is non-marginal point, the gray-scale value of this point is set to 0, the fuzzy inference rule filter result be improved.

The invention has the beneficial effects as follows:

1, in the scope of application, fuzzy inference rule edge detection method is better for salt-pepper noise effect, and after being improved by this method, the method can be applicable to Gaussian noise, and usable range is wider.

2, in rim detection integrality, this method compensate for the fuzzy inference rule edge detection algorithm deficiency that testing result is poor under strong Gaussian noise, has good noise immunity, can not lose marginal information because of noise effect, and the edge clear detected is complete.

Accompanying drawing explanation

Fig. 1 is the process flow diagram in the present invention;

Fig. 2 is the former figure of Lena in the present invention;

Fig. 3 is that in the present invention, variance is the Gaussian noise pollution Lena image of 0.03 (very noisy situation);

Fig. 4 is algorithm Lena result of the present invention in very noisy situation in the present invention.

Embodiment

Embodiment 1: as Figure 1-4, a kind of fuzzy inference rule edge detection method of improvement, the concrete steps of the fuzzy inference rule edge detection method that described use improves are as follows:

Step1, in Matlab, input piece image I (x, y), calculate difference average and the variance of each point pixel value and central point pixel value in pixel 5 × 5 window, leave three-dimensional array Ω and three-dimensional array σ respectively in ²in;

The difference average of Step2, foundation pixel value and variance, structure meets the membership function of Gaussian distribution, and carry out fuzzy filter, obtain fuzzy filter image, expression formula is as follows;

$W=e^{\left(\frac{-{\left({\mathrm{\&Omega;}}_{i,j,r,s}-{\mathrm{\&Omega;}}_{i,j}\right)}^2}{2{\mathrm{\&sigma;}}_{i,j}^2}\right)}---\left(1\right)$

Wherein, Ω _i,jbe the average of each point pixel value and central point value differences in 5 × 5 windows, be the variance of each point pixel value and central point value differences in 5 × 5 windows, the position coordinates of pixel centered by i, j, r, s ∈ {-2 ,-1,0,1,2};

Step3, Step2 is obtained fuzzy filter image be input in Matlab, calculate this fuzzy filter image each pixel 8 neighborhood gray scale difference, leave in three-dimensional array diff, then calculate POS and the NEG value on each direction;

$\begin{array}{cc}POS\left(x\right)=\left\{\begin{array}{cc}0& diff\&le;0\\ \frac{diff}{c}& 0<diff<c\\ 1& diff\&GreaterEqual;c\end{array}\right.& NEG\left(x\right)=\left\{\begin{array}{cc}1& diff\&le;-c\\ \frac{diff}{-c}& -c<diff<0\\ 0& diff\&GreaterEqual;0\end{array}\right.\end{array}---\left(2\right)$

Wherein, POS represents brightness member function, and NEG represents darkness member function, and parameter c is the gray-scale value of gray level image;

The POS value that Step4, foundation obtain and NEG value, calculate the fuzzy entropy function of this image, this function is as follows:

$H(G,c)=\frac{1}{8\&times;W\&times;H}\underset{k=1}{\overset{8}{\&Sigma;}}\underset{i=1}{\overset{W}{\&Sigma;}}\underset{j=1}{\overset{H}{\&Sigma;}}\left(S_n\right({\mathrm{\&mu;}}_{ijk}\left)\right)---\left(3\right)$

Wherein, μ _ijkfor POS value on k direction and NEG value sum, S _n() is shannon function, and this expression formula is the function about parameter c, and by asking the maximal value of this function to determine parameter c, W and H is the wide and high of image;

Step5, according to the POS value that obtains and NEG value and 16 fuzzy rules, calculate can reflect central point and adjacent 2 all belong to the degree size at edge be subordinate to angle value μ (Q); μ is the set of μ (Q), and μ is called fuzzy edge image;

Step6, determine the gray threshold of edge extracting according to μ, computing method are as follows:

T＝max((0.8×Z ^*+0.2×μ _max),μ _local)(4)

Wherein, Z ^*for the value obtained after adopting center method de-fuzzy to fuzzy edge image, μ _maxthe maximal value of fuzzy edge image μ, μ _local3 × 3 window local mean value of fuzzy edge image μ;

Step7, to compare with gray threshold T with the gray-scale value of each pixel of fuzzy edge image μ again, when the gray-scale value of the pixel in μ is more than or equal to T, judges that this point is marginal point, the gray-scale value of this point is set to 1; When the gray-scale value of the pixel in μ is less than T, judges that this point is non-marginal point, the gray-scale value of this point is set to 0, the fuzzy inference rule filter result be improved.

Embodiment 2: as Figure 1-4, a kind of fuzzy inference rule edge detection method of improvement, the concrete steps of the fuzzy inference rule edge detection method that described use improves are as follows:

Step1, in Matlab, input piece image I (x, y), calculate difference average and the variance of each point pixel value and central point pixel value in pixel 5 × 5 window, leave three-dimensional array Ω and three-dimensional array σ respectively in ²in;

The difference average of Step2, foundation pixel value and variance, structure meets the membership function of Gaussian distribution, and carry out fuzzy filter, obtain fuzzy filter image, expression formula is as follows;

$W=e^{\left(\frac{-{\left({\mathrm{\&Omega;}}_{i,j,r,s}-{\mathrm{\&Omega;}}_{i,j}\right)}^2}{2{\mathrm{\&sigma;}}_{i,j}^2}\right)}---\left(1\right)$

Wherein, Ω _i,jbe the average of each point pixel value and central point value differences in 5 × 5 windows, be the variance of each point pixel value and central point value differences in 5 × 5 windows, the position coordinates of pixel centered by i, j, r, s ∈ {-2 ,-1,0,1,2};

Step3, Step2 is obtained fuzzy filter image be input in Matlab, calculate this fuzzy filter image each pixel 8 neighborhood gray scale difference, leave in three-dimensional array diff, then calculate POS and the NEG value on each direction;

$\begin{array}{cc}POS\left(x\right)=\left\{\begin{array}{cc}0& diff\&le;0\\ \frac{diff}{c}& 0<diff<c\\ 1& diff\&GreaterEqual;c\end{array}\right.& NEG\left(x\right)=\left\{\begin{array}{cc}1& diff\&le;-c\\ \frac{diff}{-c}& -c<diff<0\\ 0& diff\&GreaterEqual;0\end{array}\right.\end{array}---\left(2\right)$

Wherein, POS represents brightness member function, and NEG represents darkness member function, and parameter c is the gray-scale value of gray level image;

The POS value that Step4, foundation obtain and NEG value, calculate the fuzzy entropy function of this image, this function is as follows:

$H(G,c)=\frac{1}{8\&times;W\&times;H}\underset{k=1}{\overset{8}{\&Sigma;}}\underset{i=1}{\overset{W}{\&Sigma;}}\underset{j=1}{\overset{H}{\&Sigma;}}\left(S_n\right({\mathrm{\&mu;}}_{ijk}\left)\right)---\left(3\right)$

Wherein, μ _ijkfor POS value on k direction and NEG value sum, S _n() is shannon function, and this expression formula is the function about parameter c, and by asking the maximal value of this function to determine parameter c, W and H is the wide and high of image;

Step5, according to the POS value that obtains and NEG value and 16 fuzzy rules, calculate can reflect central point and adjacent 2 all belong to the degree size at edge be subordinate to angle value μ (Q); μ is the set of μ (Q), and μ is called fuzzy edge image;

Step6, determine the gray threshold of edge extracting according to μ, computing method are as follows:

T＝max((0.8×Z ^*+0.2×μ _max),μ _local)(4)

Wherein, Z ^*for the value obtained after adopting center method de-fuzzy to fuzzy edge image, μ _maxthe maximal value of fuzzy edge image μ, μ _local3 × 3 window local mean value of fuzzy edge image μ;

Step7, to compare with gray threshold T with the gray-scale value of each pixel of fuzzy edge image μ again, when the gray-scale value of the pixel in μ is more than or equal to T, judges that this point is marginal point, the gray-scale value of this point is set to 1; When the gray-scale value of the pixel in μ is less than T, judges that this point is non-marginal point, the gray-scale value of this point is set to 0, the fuzzy inference rule filter result be improved.

During embody rule, for in very noisy situation, be the former figure of Lena of the present invention for Fig. 2, the Gaussian noise of Fig. 3 to be the variance in the present invention be 0.03 (very noisy situation) pollutes Lena image, use this method, as shown in Figure 4, Fig. 4 illustrates the Lena figure that the present invention is directed in very noisy situation and carries out rim detection the Lena result of method of the present invention, result can find out that its noiseproof feature is strong, almost completely can detect image border.

By reference to the accompanying drawings the specific embodiment of the present invention is explained in detail above, but the present invention is not limited to above-mentioned embodiment, in the ken that those of ordinary skill in the art possess, various change can also be made under the prerequisite not departing from present inventive concept.

Claims (1)

1. the fuzzy inference rule edge detection method improved, is characterized in that: the described concrete steps of the fuzzy inference rule edge detection method improved that use are as follows:

Step1, in Matlab, input piece image I (x, y), calculate difference average and the variance of each point pixel value and central point pixel value in pixel 5 × 5 window, leave three-dimensional array Ω and three-dimensional array σ respectively in ²in;

The difference average of Step2, foundation pixel value and variance, structure meets the membership function of Gaussian distribution, and carry out fuzzy filter, obtain fuzzy filter image, expression formula is as follows;

$W=e^{\left(\frac{-{\left({\mathrm{\&Omega;}}_{i,j,r,s}-{\mathrm{\&Omega;}}_{i,j}\right)}^2}{2{\mathrm{\&sigma;}}_{i,j}^2}\right)}---\left(1\right)$

Wherein, Ω _i,jbe the average of each point pixel value and central point value differences in 5 × 5 windows, be the variance of each point pixel value and central point value differences in 5 × 5 windows, the position coordinates of pixel centered by i, j, r, s ∈ {-2 ,-1,0,1,2};

Step3, Step2 is obtained fuzzy filter image be input in Matlab, calculate this fuzzy filter image each pixel 8 neighborhood gray scale difference, leave in three-dimensional array diff, then calculate POS and the NEG value on each direction;

$\begin{array}{cc}POS\left(x\right)=\left\{\begin{array}{cc}0& diff\&le;0\\ \frac{diff}{c}& 0<diff<c\\ 1& diff\&GreaterEqual;c\end{array}\right.& NEG\left(x\right)=\left\{\begin{array}{cc}1& diff\&le;-c\\ \frac{diff}{-c}& -c<diff<0\\ 0& diff\&GreaterEqual;0\end{array}\right.\end{array}---\left(2\right)$

Wherein, POS represents brightness member function, and NEG represents darkness member function, and parameter c is the gray-scale value of gray level image;

The POS value that Step4, foundation obtain and NEG value, calculate the fuzzy entropy function of this image, this function is as follows:

$H(G,c)=\frac{1}{8\&times;W\&times;H}\underset{k=1}{\overset{8}{\&Sigma;}}\underset{i=1}{\overset{W}{\&Sigma;}}\underset{j=1}{\overset{H}{\&Sigma;}}\left(S_n\right({\mathrm{\&mu;}}_{ijk}\left)\right)---\left(3\right)$

Wherein, μ _ijkfor POS value on k direction and NEG value sum, S _n() is shannon function, and this expression formula is the function about parameter c, and by asking the maximal value of this function to determine parameter c, W and H is the wide and high of image;

Step5, according to the POS value that obtains and NEG value and 16 fuzzy rules, calculate can reflect central point and adjacent 2 all belong to the degree size at edge be subordinate to angle value μ (Q); μ is the set of μ (Q), and μ is called fuzzy edge image;

Step6, determine the gray threshold of edge extracting according to μ, computing method are as follows:

T＝max((0.8×Z ^*+0.2×μ _max),μ _local)(4)

Wherein, Z ^*for the value obtained after adopting center method de-fuzzy to fuzzy edge image, μ _maxthe maximal value of fuzzy edge image μ, μ _local3 × 3 window local mean value of fuzzy edge image μ;

Step7, to compare with gray threshold T with the gray-scale value of each pixel of fuzzy edge image μ again, when the gray-scale value of the pixel in μ is more than or equal to T, judges that this point is marginal point, the gray-scale value of this point is set to 1; When the gray-scale value of the pixel in μ is less than T, judges that this point is non-marginal point, the gray-scale value of this point is set to 0, the fuzzy inference rule filter result be improved.